Question

tan（x+y）的隐函数的导数

Answer 1

问：tan（x+y）的隐函数的导数

答：你好！y=tan(x+y) 两边求导,用公式(tany)=sec²y*y'y'=sec²(x+y)(x+y)'y'=sec²(x+y)(1+y')y'=sec²(x+y)+y'sec²(x+y)y'[1-sec²(x+y)]=sec²(x+y)y'=sec²(x+y)/[1-sec²(x+y)]=-sec²(x+y)/tan²(x+y),用公式(1-sec²x)=-(sec²x-1)=-tanx=-1/cos²(x+y)*cos²(x+y)/sin²(x+y),约掉cos²(x+y)=-1/sin²(x+y)=-csc²(x+y)